This paper might be a pre-copy-editing or a post-print ...senseable.mit.edu/papers/pdf/20100701_DiSabatino... · partimento di Scienza deiMateriali, Laboratoriodi Climatologia e Meteorologia,

This paper might be a pre-copy-editing or a post-print author-produced .pdf of an article accepted for publication. For the

definitive publisher-authenticated version, please refer directly to publishing house’s archive system.

Construction of Digital Elevation Models for a Southern European Cityand a Comparative Morphological Analysis with respect to Northern

European and North American Cities

SILVANA DI SABATINO, LAURA SANDRA LEO, AND ROSELLA CATALDO

Dipartimento di Scienza dei Materiali, University of Salento, Lecce, Italy

CARLO FILIPPO RATTI

Massachusetts Institute of Technology, Cambridge, Massachusetts

REX EDWARD BRITTER

Senseable City Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts

(Manuscript received 15 September 2008, in final form 18 February 2010)

ABSTRACT

A morphometric analysis of a southern European city and the derivation of relevant fluid dynamical pa-

rameters for use in urban flow and dispersion models are explained in this paper. Calculated parameters are

compared with building statistics that have already been computed for parts of three northern European and

two North American cities. The aim of this comparison is to identify similarities and differences between

several building configurations and city types, such as building packing density, compact versus sprawling

neighborhoods, regular versus irregular street orientation, etc. A novel aspect of this work is the derivation

and use of digital elevation models (DEMs) for parts of a southern European city. Another novel aspect is the

DEMs’ construction methodology, which is low cost, low tech, and of simple implementation. Several building

morphological parameters are calculated from the urban DEMs using image processing techniques. The

correctness and robustness of these techniques have been verified through a series of sensitivity tests per-

formed on both idealized building configurations, as well as on real case DEMs, which were derived using the

methodology here. In addition, the planar and frontal area indices were calculated as a function of elevation.

It is argued that those indices, estimated for neighborhoods of real cities, may be used instead of the detailed

building geometry within urban canopy models as those indices together synthesize the geometric features of

a city. The direct application of these results will facilitate the development of fast urban flow and dispersion

models.

1. Introduction

In recent years we have witnessed an increase of ur-

banization worldwide. Over 50% of the world’s pop-

ulation (almost 80% in the United States and about 70%

in Europe) live in cities and this ratio is still increasing.

This is particularly evident in developing countries un-

dergoing rapid urbanization: between 2000 and 2030, the

urban population in Africa and Asia is set to double and,

by that same year, urban dwellers will make up about

60% of the world’s population (United Nations, World

Population Prospects: The 2006 Revision, 200 AU17).

Urbanization affects the environment within and be-

yond cities. Many economic and social activities, gov-

ernmental operations, and extensive infrastructures are

located in cities or in nearby areas. Air quality in urban

areas is continually deteriorating because of many of these

activities, particularly the increase of vehicular traffic.

Moreover, the larger consumption of energy in cities may

contribute to the formation of heat islands modifying the

urban climate and causing pollutant entrapment zones.

Pollution can injure human health, harm the environ-

ment, and cause building deterioration and property dam-

age. For these reasons, accurate prediction of pollution

jamC2117

Corresponding author address: Dr. Silvana Di Sabatino, Di-

partimento di Scienza dei Materiali, Laboratorio di Climatologia e

Meteorologia, University of Salento, Via Monteroni, 73100 Lecce,

Italy.

E-mail: [email protected]

JOBNAME: JAM 00#0 2010 PAGE: 1 SESS: 8 OUTPUT: Mon Apr 26 20:49:55 2010 Total No. of Pages: 20/ams/jam/0/jamC2117

MONTH 2010 D I S A B A T I N O E T A L . 1

DOI: 10.1175/2010JAMC2117.1

� 2010 American Meteorological Society

Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

dispersion and of urban air quality are becoming more

and more important with respect to legal regulations

concerning acceptable pollutant levels, environmental

planning, and the health of the citizens. Additionally,

these and other related issues demand substantial stud-

ies of the impact of urban growth on climate change.

In particular, it is of interest to understand how the wind

and turbulence fields change above and within the city as

a consequence of airflow interaction with the urban ag-

glomeration. In the idealized case of arrays of buildings of

regular size and shape, the resulting flow structure can

be roughly categorized in terms of the spacing among

buildings into three flow regimes, which are: isolated ob-

stacle flow, wake interference flow, and skimming flow

(Oke 1988). In the case of a real city, the complex urban

texture generates more complicated flow patterns with

occurrence of flow separation. Numerical modeling, such

as computational fluid dynamics (CFD) including large

eddy simulation (LES) models, should be used for the

prediction of such flows. However, in most cases, it is still

not practical to calculate the flow around every obstacle.

For this reason, a parameterization to represent the dy-

namical effect of an urban area is still required as it arises

from many studies available in the mesoscale modeling

community (see, e.g., Martilli et al. 2000; Brown 2000;

Otte et al. 2004). The level of topographical or building

detail depends upon the modeling scale, increasing from

the regional scale, through the city and the neighbor-

hood scales, up to the street scale (Grimmond and Souch

1994; Britter and Hanna 2003).

Various methods for determining aerodynamic pa-

rameters exist. Comprehensive direct measurements of

wind and turbulence fields in cities are difficult. In fact,

they require observations taken at several horizontal

positions within the city and at various vertical levels,

some of them well above the average building height. As

an alternative, morphometric methods express the cit-

ies’ aerodynamics characteristics in terms of average

building height (H), planar area index (lp), frontal area

index (lf), and other measurable parameters related to

the urban morphology (e.g., Cionco and Ellefsen 1998;

Grimmond and Oke 1999).

Urban morphometric analyses have been conducted

more widely in the United States (Burian et al. 2007)

than in Europe, especially in southern Europe. Such

analyses require the characterization of the built ele-

ments, which is difficult because of the irregularity and

asymmetry of the associated shapes. This heterogeneity

can be found at different scales within the city and among

cities, and the variability is partially related to geographic

positioning, geomorphologic structure, and historical

background of the specific territory in which the city has

developed. For example, European cities have grown with

successive additions of neighborhoods from the city center

to the suburbs (Long et al. 2003). ‘‘Modern cities are often

characterized by clusters of high rise buildings and wider

streets, meanwhile older cities often have very narrow

streets and densely-packed, few-storey high buildings’’

(Kastner-Klein et al. 2004). We are still some way from

a systematic study that provides an extensive classification

of different city types based on morphometric criteria.

In previous work, building statistics have been calcu-

lated according to different urban land use categories

such as residential, commercial, industrial, and down-

town core areas. Grimmond and Oke (1999) as well as

Burian et al. (2007) performed such studies on several

North American cities. Similarly, other authors derived

relevant flow and dispersion parameters linked to the

urban morphology for parts of some northern European

cities, such as London, Toulouse, and Berlin (e.g., Ratti

et al. 2002, 2006). However, little attention has been

directed toward cities in southern European and Medi-

terranean regions even though their morphological, geo-

graphical, historical, and societal characteristics would be

of considerable scientific interest, especially given their

unique climate (e.g., Camuffo et al. 2000; Bolle 2003).

In the past, one of the main difficulties of the morpho-

metric approach, particularly outside the United States,

was the limited availability of data describing the urban

texture. Grimmond and Souch (1994) were among the

first researchers to develop an urban DEM; a few years

later Grimmond and Oke (1999) and others (e.g., Burian

et al. 2002; Ratti et al. 2000) employed this methodology

to determine the aerodynamic properties of urban sites.

Burian et al. (2004) reviewed presently available data

sources and data-collecting methods. Many techniques can

be used to construct DEMs. Among those there are re-

mote sensing techniques, such as satellite imagery (Tacket

et al. 1991), aerial photography (Muller et al. 1999), ste-

reophotography, and plane-mounted lidar (Baltsavias

1999). Regardless of the technique used, DEMs are just

two-dimensional (2D) matrices (raster structure) of height

values where the position of each matrix element is im-

plicitly associated with planar spatial coordinates. There-

fore, DEMs contain three-dimensional (3D) information

based on a 2D structure that can be stored in different

formats. Among these, the raster image is a convenient

format as it is commonly used and easily readable with

most freely available software packages. Each pixel of the

raster image represents a value of building height and can

be displayed in shades of gray. However, DEMs are not

yet available for many areas, in part because of their cost.

In this paper we show how raw data of building heights

can be obtained at low cost to construct DEMs. We de-

rive DEMs for parts of a southern European city to show

their sensitivity to image resolution and data formats; we

2 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 00


Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

proceed to compare and comment on these DEMs with

those available to us for other areas. DEMs are analyzed

to calculate a number of morphological parameters.

Specifically, we determine H, lp, and lf, and then calcu-

late the roughness length z0 and other parameters for the

city of Lecce, Italy, as an example of a typical southern

European or Mediterranean city. The calculation is based

on extensions of some available algorithms based on

image processing techniques developed within the Mat-

lab environment (MATLAB 199AU2 7) as discussed by Ratti

et al. (2000) and Ratti and Richens (2004). All algorithms

are evaluated by means of sensitivity tests performed on

idealized DEMs made up of simple arrangements of cu-

bic and rectangular buildings for which an analytical

calculation of the morphometric parameters is possible.

Three urban DEMs corresponding to different parts

of the city of Lecce are analyzed and the morphometric

and aerodynamic properties are compared with those

of some parts of three northern European and two

North American cities, noting their similarities and dif-

ferences and their possible effects on wind and dispersion

characteristics.

The Lecce study areas are described in section 2. Sec-

tion 3 describes how DEMs were constructed and how

the morphometric parameters were extracted using im-

age processing techniques. Image resolution sensitivity

tests are also discussed in this section. Section 4 shows the

new algorithms for the calculation of lf (z) and its vali-

dation. The results are discussed in section 5, conclusions

are presented in section 6, and an appendix is included

with details of the various image sensitivity tests.

2. Study areas

The study areas are located in Lecce (408239N, 188119E),

a medium-size city, typical of southern Italy and of the

eastern Mediterranean area. The city is in the middle

of a narrow peninsula about 40 km wide and 70 km long.

Lecce has about 100 000 inhabitants and is known for

its important cultural building heritage. Urban pollution

sources, such as heavy traffic and domestic heating as

well as the presence of a large power plant and an in-

dustrial site about 50 km from the city produce poor

air quality in Lecce. FF1 igure 1 shows the location of the

city (Fig. 1a) together with these two major pollutant

sources (Fig. 1b). The city has an overall rectangular

shape (7 3 5 km) with the longer side along the northeast/

southwest direction. The morphological structure reflects

that of a southern European and Mediterranean city. It

has developed around the historical center bounded by

pre-Roman walls that enclose an area of about 2 3 1.5 km.

This older part of the city is characterized by densely

packed buildings of two or three stories with irregular

footprints, flat terrace-type roofs, and internal courtyards.

Several churches and small courts separated by twisted

alleys are also present.

Newer parts of the city generally have taller buildings

that are mainly residential apartments or commercial

buildings. Buildings here have a more regular shape

than those in the historical center and they are less ir-

regularly distributed but equally densely packed. Some

minor industrial sites about 10 km from the city center

are not considered here.

In this study we focus on three neighborhoods of 400 3

400 m. This size has been chosen to facilitate the com-

parison with previously analyzed DEMs. All three neigh-

borhoods are part of downtown Lecce where commercial,

public office, and residential buildings are mixed together.

Two of the areas (named Le1 and Le2) are in the same

part of the city and include tall commercial buildings of

rather regular shape (a rectangular footprint). In contrast,

the third area (named Le3) includes the Public Gardens

where about 140 trees up to 20 m high cover a surface

that is about 3% of the total area. Le3 includes a small

part of the historical center, where buildings are arranged

FIG. 1. Aerial photo by Google Earth of (a) Lecce and

surrounding areas with (b) the locations of the main pollutant

sources in Taranto and Brindisi.



Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

in a very complex manner with roads typically not per-

pendicular to each other. Overall this site has a less regular

structure than the other two study areas. The building

density is also greater than the other two. Most buildings

in this area are public, including schools. This area was

selected as it is different in structure from the other two

and also because it is among the most polluted of the

city’s neighborhoods. The choice of Le1 and Le2 was

motivated by their planar building density being similar

to those of London and Toulouse previously analyzed

by Ratti et al. (2000).

3. Methodology

The methodology followed for the DEMs’ construc-

tion and their subsequent analyses starts with the col-

lection of raw measurements of the building heights and

proceeds with their processing and transformation into

various image formats.

a. Building-height data collection

Building-height data collection took about three months

for the three city areas. Planar dimensions of the buildings

were available from 1:2000 scale planar maps stored in

digital form. All buildings on the map were checked and

identified on site. Building footprints were in some cases

inaccurate and were corrected by measuring them on site.

Building heights were measured from the ground level

from two sides when possible. Building-height data were

measured using a distance meter Leica DISTO mounted

on a tripod at ground level, positioned 2–3 m from the

building facxade. This instrument is a laser diode consist-

ing of a laser pulse of known frequency split into a refer-

ence beam and a measurement beam by a system of

mirrors. Because of the delay time between the reference

ray and the external trajectory of the ray of measurement,

the difference of phase between these two signals is

proportional to the distance between the distance meter

and the reflecting surface. To make use of the full nom-

inal accuracy of the instrument (2 mm) we placed it in

front of each building facade and performed sets of three

auxiliary measurements. F F2igure 2 shows the typical in-

strument setup with the three auxiliary measurements.

The figure also shows photographs of one of the street

canyons and the DISTO instrument. As the laser mea-

suring points have to be on a straight line in a vertical

plane, the use of the tripod avoids the possibility of shaky

measurements. The second auxiliary measurement must

be made perpendicular to the desired length. This can be

done by using a bubble level allowing for a simple hori-

zontal leveling of the instrument as the distance meter is

provided with a magnetic support for attaching acces-

sories. The estimated building height is the result of the

three measurements combined through their squared,

triangle geometrical relationships.

While the distance meter has a resolution of 2 mm, the

laser dot resolution can be up to few centimeters for each

set of measurements. Errors introduced by the operator

FIG. 2. Illustration of building measurement setup. Labels 1, 2, 3 correspond to the three

series of auxiliary measurements used to determine the (left) building height; (upper right)

distance meter instrument DISTO; (bottom right) typical street canyon in Lecce.



Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

can be significant for very tall buildings as some difficul-

ties may arise in performing the auxiliary measurement

along a vertical plane (label 1 in Fig. 2). The instrumental

errors are always negligible in comparison with those

introduced by the operator. To minimize them, the dis-

tance meter was equipped with a telescopic viewfinder

with fourfold magnification.

By performing some tests on building of known height

we estimated that, for building heights less than 40–50 m,

errors associated with the overall building height mea-

surement are less than 1 m. Such measurement errors

were considered acceptable for our research purposes.

For the representation of buildings on the map, some

approximations were made:

d a porch inside a group of buildings was not represented;d sparse trees, walls, roof overhangs, turrets of staircases

at the top of some buildings, buildings under construc-

tion, etc., were neglected;d over the whole study area, the road level was assumed

to be horizontal;d the representation of the dome of a church was also

approximated. It was drawn as a cylinder of the di-

ameter of the dome, but of smaller height to simulate

a cylinder of similar volume;d the trees of the Public Gardens were represented by

a square plan shape with a constant height equal to the

average tree height.

b. Construction of the DEMs

The construction of the actual DEMs consisted in dis-

playing individual building heights on the original planar

maps and in forming new vector layers where the basic

units to be mapped were structures of different heights.

Every building is described by a 2D polygon with specific

attributes corresponding to its footprint and rooftop el-

evation. DEMs of the three study areas were manipu-

lated using ESRI ArcView Gis 3.2 tools to convert them

into a raster image; that is, in a form appropriate for

the application of image processing techniques. F F3igure 3

shows the various phases of the DEM construction from

the aerial photograph to the DEM in raster form. The

intermediate phases consist of using planar building maps

in digital form, editing building footprints if necessary

with CAD software, adding building-height measure-

ments to them and representing the maps as a vector

DEMs. Once the DEMs are in raster form they can be

analyzed using image processing techniques.

In this study we compute urban morphometric pa-

rameters (explained in the next section) by using pre-

viously developed computer programs and by developing

new ones within Matlab’s Image Processing Toolbox in

which images were represented as square matrices and

pixels were coded using 8 bits (though higher resolutions

could be used in principle).

In the vector to raster transformation, care should be

taken in choosing the appropriate correspondence be-

tween image pixel and building height. This was done by

using a grayscale so that each pixel has a level of gray

proportional to the building height. For 8-bit images this

corresponds to 256 levels of gray. Each image has its own

scale so that the value 255, displayed as white on a raster

structure, is assigned to the road level (0 m) and the

0 value corresponding to the black color is assigned to

the maximum building height. Typically, if building-

height accuracy is 1 m, not all 256 values of gray are used

because buildings normally are shorter than 255 m. In-

stead, particular shades are used for a given building

height in such a way to minimize the errors arising from

the conversion from the grayscale to the building height.

The choice of the shade interval can be made according

to the building-height distribution histogram as done in

remote sensing data representations. This way of assign-

ing the pixel level makes full use of the range of gray

shades and more clearly represents building heights.

A further point to make concerns the choice of the

pixel size (this is separate from the issue above). One of

the problems related to the DEM construction in a raster

FIG. 3. Illustration of the various phases of DEM’s construction. Starting from (left) aerial photo of the area, (right) the raster DEM is

constructed by (second from left) using planar maps in digital form and by (third from left) converting the vector DEM into an image.



Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

form, obtained as a data conversion from vector struc-

tures, is that the pixel size should be small enough not to

affect the positional accuracy of building footprints. This

could be solved following general rules adopted in digital

photogrammetry. On the other hand, the size of the pixel

should not affect the values of the morphometric pa-

rameters to be calculated. From the theoretical point of

view, one should choose the pixel size that satisfies both

requirements and which is the lower of the two. However,

in the context of this work, it is sufficient that the choice

of the pixel size is made only in relation to the calcula-

tion of the morphometric parameters without taking

into account the problem of the positional accuracy.

This is further addressed below.

c. Estimation of morphometric parametersfor three areas

The originally derived DEMs for the three areas Le1,

Le2, and Le3 were analyzed to calculate building sta-

tistics as well as several building morphometric param-

eters. In particular, lp, lf, and zH (the average height

weighted with building frontal area) are calculated as:

lp

5

�i

Ap,i

AT

, (1)

lf(u) 5

�i

Af ,i

(u)

AT

, (2)

zH

(u) 5

�i

HiA

f ,i(u)

�i

Af ,i

(u), (3)

where Hi and Ap,i are respectively the height and the

planar area of the ith building, while Af,i(u) is its frontal

area perpendicular to the wind direction u. The AT is

the total site planar area, lf represents the total area of

buildings projected into the plane normal to the incoming

wind direction and is a function of orientation. For a

given wind direction, lf is smaller if the wind angle is

oblique, rather than perpendicular, to the front face of the

building. That is, Af,i is multiplied by a sin(u) function

dependent on wind angle relative to that building face.

In addition, we calculated four other statistical pa-

rameters: the average building height and its standard

deviation, and the average building height weighted

with the planar area and its standard deviation. The last

two, more meaningful from the fluid dynamics point of

view, are defined as:

H 5

�i

HiA

p,i

�i

Ap,i

, (4)

s 5

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�

i(H

i�H)2

N � 1

vuut. (5)

Starting from these parameters, we computed the zero-

plane displacement height, zd, and roughness length, z0,

using the equations derived by Macdonald et al. (199 AU38):

zd

H5 1 1 (l

p� 1)a�l

P , (6)

z0

H5 1�

zd

H

� �exp �

0.5bCD

lF

k21�

zd

H

� �� 0.5( )

, (7)

with a 5 4.43, b 5 1.0, k 5 0.4, CD ; 1.

As discussed previously, the particular technique used

to derive those building morphological parameters re-

quires an assessment of the influence of image resolution

on the results. This is particularly relevant when using

those parameters within urban dispersion models. One

may find that an error of 10% on the calculated param-

eters is acceptable given the large approximations usually

made in those models. More importantly, one may find

that a variation of 10% in the value of the building

morphological parameters is irrelevant from the fluid

dynamics point of view. This needs to be evaluated

through detailed numerical flow simulations.

As described in the previous subsection, the con-

struction and analysis of DEMs consists of converting

vector data into a raster image and then storing this

image in a specific format. This format should be chosen

in such a way to avoid, or at least minimize, loss of in-

formation relevant for urban morphometry analyses.

For the same reason, image spatial resolution is impor-

tant, also because it can affect the edge detection oc-

curring in several algorithms; for example, those related

to lp and lf calculations. As a consequence, it is ap-

propriate to investigate how the image storage format

may affect results before interpreting them. Indeed,

even when DEM analysis by image processing tech-

niques has been carried out (i.e., Ratti et al. 2006),

a suitable sensitivity analysis has not always been done.

We performed several tests on many building arrange-

ments of different complexity to investigate how specific

image formats, such as TIFF, BMP, JPEG, and GIF, as

well as the image spatial resolution influence the accu-

racy of the calculated parameters. Details on the various

tests and specific results of the sensitivity analyses are



Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

reported in the appendix. In general, all formats except

JPEG do not influence results but the image resolution

does. The way image resolution affects the calculation

accuracy is rather complex, because it depends on the

specific building arrangements, shape, and orientation.

The various tests performed suggest that to minimize

errors, the original DEMs should be rotated in such

a way as to get most of the building facades aligned with

the external raster frame. This procedure allows us to

reduce the effect of changing the intrinsic positional

regularity of the pixels.

The sensitivity analysis shows that the accuracy of the

lp parameter improves with increasing image resolu-

tion. This does not happen for all other parameters,

which, instead, do not behave linearly with image reso-

lution and appear to be more dependent on the specific

building arrangement rather than the image resolution.

To identify a general rule for handling errors due to

image resolution, it is reasonable to adopt the criterion

of choosing that image resolution that does not affect

the value of lp. Errors on the other building morphology

parameters are then calculated on the basis of the cho-

sen image resolution. TT1 able 1 summarizes the errors re-

lated to all calculated parameters for the case when lp

agrees with its theoretical value, at least within the first

two significant digits. The errors can be large on both

roughness length and displacement height. We antici-

pate that errors are more significant for cities that tend

to have irregular building arrangements and orienta-

tions as it is typically the case of southern European/

Mediterranean cities.

4. The frontal area index as a function of elevation

As a principal objective of this work, we now furnish

some guidelines on the suitability of the calculated

morphometric parameters within urban flow and dis-

persion models. Starting from the idea that a city can be

represented as a superposition of neighborhoods each

characterized by some lambda parameters, one may

look for useful representations of the city’s neighbor-

hoods in those models. Recent literature has shown how

wind flow and dispersion characteristics can be derived

from morphometric parameters, which are formulated as

a function of the elevation z. For example, Di Sabatino

et al. (2008) developed a simple model for spatially

averaged wind profiles within and above real urban

canopy layers where buildings are represented by the

frontal area index as a function of z, lf (z). This param-

eter has been calculated also by Burian et al. (2007) for

several cities in North America. However, lf (z) deri-

vation from image processing techniques has not been

explicitly addressed. As described in Ratti et al. (2006),

the key element of the algorithm to calculate lf for

a given wind direction u is the calculation of the overall

building facade area along that direction. This involves

the derivation of the unit vector perpendicular to the

DEM surface on each pixel. By applying geometric re-

lationships, lf is calculated by summing all individual

building facxade areas projected into the given wind di-

rection. A more detailed description of the algorithm

can be found in Ratti et al. (2006).

We now present a modification of this algorithm in

order to calculate the variation with height of the frontal

area index, lf (z, u), defined as:

lf(z, u) 5

�i

dAf ,i

(z, u)

AT

. (8)

For a given wind direction u and a constant increment

height interval Dz, dAf,i(z) indicates the portion of the

building frontal area in the region between z and z 1 Dz.

In other words, dAf,i(z) is equal to Wf,iDz, where Wf,i is

the width of the facade perpendicular to the wind of the

ith building at the elevation z. F F4igure 4 illustrates the

definition of the building scales: H (height), W (width),

and L (depth).

The original algorithm for lf (u) is modified in order to

select those pixels within the layer between z and z 1 Dz

and to apply to those pixels the usual procedure for the

calculation of lf. The result is such that the sum of lf

values calculated for every Dz coincides with the total

frontal area index for the given wind direction. The

value of Dz should not be smaller than the building

height accuracy which for our case is 1 m.

The new algorithm was evaluated through several

tests on idealized building arrangements for which a

theoretical calculation of the morphometric parameters

was possible. As an example, F F5ig. 5 shows the results for

lf (z) profiles calculated for very simple cases and their

comparison with theoretical values. The first case is that

TABLE 1. Summary of image resolution tests on mean values of some morphometric parameters. The word ‘‘correct’’ means that lp is

computed accurately within two significant digits.

lf H zd z0

Estimated error based

on the ‘‘correct’’ lp values

0.7% (up to 13% for

complex geometries)

0.3%–0.4% 0.03% (up to 2% for

complex geometries)

7% (up to 11% for

complex geometries)



Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

of a single square building of 150 3 150 pixels and 32 m

height on total area of 256 3 256 pixels. The second case

consists of four rectangular buildings. From top left,

clockwise, their planar dimension were 50 3 70 pixels

(height 5 10 m), 50 3 30 pixels (height 5 5 m), 50 3 20

pixels (height 5 5 m), 30 3 50 pixels (height 5 10 m) on

total area of 256 3 256 pixels. As expected, in the first

case lf (z) is constant while in the second case it shows

a step change. The agreement between the computed

lf (z) profiles and the theoretical ones is excellent. For

those simple regular geometries and building arrange-

ments the percentage error is negligible and beyond the

third significant digit. Overall, the evaluation performed

on simple building arrangements allowed us to apply

with confidence the developed lf (z) algorithm to real

building configurations.

5. Discussion and results

In this section, DEMs originally derived following the

methodology previously described for the three areas of

Lecce, Le1, Le2, and Le3, are presented, discussed, and

compared with three DEMs of three northern European

cities and two DEMs of North American cities. The choice

to compare cities according to their geographic location

was considered relevant from the meteorology and cli-

mate points of view but other criteria could be used. The

approach used in our analyses is not dependent on the

specific choice of north–south cities, though specific re-

sults will be presented here in this framework.

a. Southern European DEMs: General description

FF6 igure 6 shows DEMs in grayscale for the three areas

of Lecce. We reiterate that each image has its own scale

and that black corresponds to the maximum building or

tree height in that specific area (32 m for Le1 and 28 m

for the other two). To facilitate the interpretation of these

images, building distribution histograms are shown for

the three areas in F F7ig. 7, with and without the trees of the

Le3 area. To more clearly emphasize the natural break-

down of building distribution in each neighborhood,

a height interval of 3 m, which is typical for each storey in

Lecce, was chosen. Focusing on the building height dis-

tribution only, without trees, it can be seen that Le1 is the

most uniform among the three areas, with a similar num-

ber of short and tall buildings. Le2 has the highest number

of short buildings and few tall buildings. Le3 is charac-

terized by buildings of intermediate height. Overall, this

area has a bell-shape building-height distribution around

a mean value of 10–12 m, corresponding to three to four

stories. This distribution is altered substantially by the

trees. Trees act as additional obstacles to the flow, and

therefore, they have been included in the basic building

height statistics and, most importantly, in the derivation

of fluid dynamics parameters as discussed in the next

sections.

b. Southern European cities versus northernEuropean and North American cities:First analysis

DEMs shown in Fig. 6 have been analyzed using the

image processing technique to derive the morphometric

parameters that have been illustrated in detail in section

3 and 4. Summarized in F F8ig. 8, the results are compared

with those of existing DEMs of parts of three northern

European and two North American cities, which have

been recalculated with the exception of Los Angeles, for

which we used values from Burian et al. (2002), directly.

From Fig. 8 we observe a substantial difference among

the five urban morphometry datasets. European cities

have an average building height H of 12–20 m and s/H

values typically between 0.3 and 0.4. On the contrary,

the North American cities have a much larger range for

both parameters. For European cities the planar area

index lp is around 0.40, a reflection of their typical layout

with buildings close to each other and narrow streets. For

the two North American cities lp is considerably smaller.

This might not be the case for all North American cities

because such cities as Boston (Massachusetts), New York

(New York), Chicago (Illinois), and others have a much

larger lp (Burian et al. 2007) more similar to European

cities. Differences are larger for the lf parameter: it is the

largest for Lecce (;0.5), smaller (;0.3) for northern

European cities, and the smallest (;0.25) for the two

cities in North America.

An additional way to derive building shape informa-

tion is by looking at polar diagrams of lf variation with

wind direction u. As an example, F F9ig. 9 reports lf (u) for

FIG. 4. Illustration of building scales. The horizontal dimension of

the building facade perpendicular to the incoming wind direction is

always denoted as W.



Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

Le2, Toulouse, and Salt Lake City, chosen to represent

the three geographic regions (southern Europe, north-

ern Europe, and North America) investigated in this

study. The first two cities have a circular symmetry, with

lf (u) almost constant with wind direction, while Le2 has

an increase in the north–south direction because most

building facades are oriented east to west. In addition to

the particular shape of lf with orientation, the plot im-

mediately shows the comparative difference in frontal

area densities among the cities investigated. It further

emphasizes the higher building densities of European

cities with respect to the ones in North America.

As previously discussed, we also calculated H, the

average building height, and zH , the building-height

weighted with the building frontal area. As pointed out

by Ratti et al. (2002), zH

is the parameter that, in prin-

ciple, should be used in the calculation of the aero-

dynamic roughness. This is because it explicitly accounts

for some features of building shape, synthesizes the overall

resistance to the wind, and, in this respect, is fluid dy-

namical relevant. By comparing the two building-height

averages for the DEMs, we see that zH is slightly smaller

than H for Le1 and Le2, and typically larger for all

DEMs analyzed. The difference between the two building-

height averages is much larger for the two North Ameri-

can cities, with respect to the other DEMs. This is a first

indication that the overall building frontal area of the

European cities investigated here is smaller than that of

the two North American cities. This also indicates build-

ings which are wider rather than taller in these European

cities. The difference between H and zH

is reflected in

the derived zero-plane displacement height, zd, and the

roughness length z0, calculated with Eqs. (6) and (7).

First of all, zd and z0 calculated with zH in place of H are

not significantly different for the European cities. The

difference ranges from about 3% for Toulouse and London

to 9% for Berlin. Instead, significant differences are

observed for the DEMs of the two North American cities

for which the use of zH

instead of H in the z0 calculation

leads to an increment of about 46% for Salt Lake City and

68% for Los Angeles. This and the z0 results for Lecce are

consistent with Ratti et al. (2000) in that, although the use

of zH in Macdonald’s formulae is generally appropriate,

it is not adequate for the North American cities analyzed

FIG. 5. The lf (z) vertical profiles and comparison between theoretical values [lf (z)theor] and

the ones [lf (z)alg] calculated using the image processing algorithms; values refer to winds

coming from the north.



Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

here. The reason for this is that Macdonald’s formulae

have been derived for cubic building arrays. They tend to

underestimate z0 for real cities, because those formulae do

not take into account building-height variability. The use

of zH is appropriate for cities characterized by relatively

large lp values. If lp is very small, as in downtown areas

of American cities, the use of zH is not required. This is

confirmed by the agreement between the z0 value for

downtown Los Angeles, obtained by Ratti et al. (2002),

using H and independently calculated by Burian et al.

(2002). In general, the size of the northern European

and Lecce sites (400 3 400 m), used in this study, would

not be large enough to perform a z0 calculation; how-

ever, this simplification can be accepted as these sites

FIG. 6. DEMs of the three areas of Lecce, named (a) Le1, (b) Le2, and (c) Le3.

FIG. 7. Histograms of building heights for the three areas (left) including trees and (right) without trees of

the Le3 area.



Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

may be considered representative of larger urban areas

with similar morphometric characteristics or neighbor-

hoods with similar lambda parameters. It should be

pointed out that even though the roughness length, cal-

culated solely on the basis of geometric considerations,

might be important in the derivation of some flow char-

acteristics in urban environment applications, the use of

z0 is questionable. In general, the use of z0 in urban flow

and dispersion models should be avoided or limited. Its

determination is controversial because of the intrinsic

difficulty linked to limited fetch, typical in urban areas,

which prevents the flow to be in equilibrium with the

changing surface (Belcher et al. 2003). It is important to

bear in mind that the derivation of z0 based on geo-

metrical considerations only, is a first estimate, but its

aerodynamic properties need to be evaluated on a case

by case basis. Additionally, doubts remain about the

suitability of Macdonald’s formulae for z0 in complex

geometries. For this and other reasons, it is worth in-

vestigating other building morphometry parameters that

can replace, among others, the use of z0 in urban flow and

dispersion models, as well as in urban representations

within mesoscale models. Obviously, the choice of a par-

ticular set of building statistical parameters depends upon

the specific application. In the following, we show how lp,

and lf as a function of elevation, are suitable for repre-

senting a city or neighborhoods in urban canopy models

and mesoscale flow models. Obviously, other choices to

represent a city based on morphometric parameters can

be made. For example, one may use lookup tables of

building and vegetation descriptors, including fractional

weights of small versus tall buildings, vegetative fraction,

FIG. 8. Comparison of building statistics and morphometric parameters for various DEMs of portions of Lecce,

three northern European cities, and two U.S. cities. For Los Angeles (Burian et al. 2002) calculations were made for

the downtown (D), the residential (R), and the industrial (I) areas; zd and z0 parameters are calculated using both

Macdonald’s et al. (1998AU9 ) equations and Raupach (1994) equations (values in parenthesis). The overbar denotes

a value averaged over all azimuths with the exception of H that does not depend on wind direction.



Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

etc., as well as their spatial variations. In this context it is

important to include intracity variations among neigh-

borhoods through the variation of the lambda descriptors.

An alternative way to describe a city is in terms of its

population density and distribution. This might be used to

derive anthropogenic heat fluxes within the city. Studies in

this direction have been initiated by several research

teams (Ching et al. 2009) with a focus on cities in North

America. Studies on city’s morphology and city’s catego-

rization based on the building distribution and other pa-

rameters in Europe and in other continents are isolated

and far from being comprehensive.

c. Southern European cities versus northernEuropean and North American cities:Further analysis

As discussed in the previous sections, lambda pa-

rameters lp, and lf, as a function of elevation, can be

used directly in flow and dispersion models as recently

done by Di Sabatino et al. (2008) and Solazzo et al.

(2010, manuscript submitted to Bound.-Layer MeteorAU4 .).

Even though the building statistics of city’s portions il-

lustrated in this study is too limited to allow any gener-

alization, we argue that the direct comparison of lambda

parameters can be used to infer city building structure

(wider or taller buildings) when detailed building data are

not available. Also lf (z) and lp(z) synthesize the vertical

distribution of a city. This is separate from having de-

tailed building geometry. Specific information about

building arrangements within urban areas or neighbor-

hoods as well as building shapes can be derived directly

from the analysis of lf (z) profiles as shown in FF10 ig. 10. We

reiterate that lf (z) describes the variation of the frontal

area density with height, which illustrates the resistance

to the wind at various heights. This has direct implica-

tions on drag force calculations at various heights.

Looking at Fig. 10, we observe a spike close to the origin,

due to the presence of tall buildings. This spike is very

pronounced for the North American cities that typically

have skyscrapers in their central business district. It is

less evident for cities in northern Europe, and absent for

Lecce, where building heights show little variation.

Again, any generalization should be avoided because

those features reflect those of the datasets analyzed.

However, some broad indications of the different city

configurations in the three geographic regions consid-

ered can be extracted based on Fig. 10. There is an in-

dication of larger packing densities in Lecce with wide

and low buildings. Note that all the profiles for lf (z) are

calculated for winds from the north. This particular

orientation was chosen as winds blow primarily from this

direction. The results may be easily extended to other

wind directions. Similar curves are obtained for lp(z)

profiles as shown in F F11ig. 11.

If we focus on the three Lecce areas, we see that the

lf(z) profile for Le1 has a slightly different curvature than

Le2 and Le3 profiles, which, in turn, are more markedly

FIG. 9. Polar diagram showing the variation of lf with wind

orientation for Le2, Toulouse, and Salt Lake City.

FIG. 10. Comparison of lf (z) profiles for (a) the European

datasets and (b) the U.S. datasets. (bottom) The Toulouse dataset

chosen for direct comparison with the two U.S. cities.



Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

discontinuous. This is of interest for investigation of

intracity variations of the lambda parameters, consid-

ering that Le1 and Le2 are adjacent areas. Similar con-

siderations can be made from lp(z) profiles. Overall,

profiles are more similar among the European cities

than those for Los Angeles and Salt Lake City. This may

be an indication of common features among the Euro-

pean cities, which are generally more compact and less

regular than the ones in North America. Other obser-

vations can be made from the derived statistical pa-

rameters keeping in mind that all datasets with the

exception of Le2 include building heights only without

trees or vegetation, and therefore some care should be

paid in using the results directly.

d. Toward a synthetic representation of a city

The choice of a particular set of building statistical

parameters to represent a city depends upon the specific

application, which needs to be evaluated before using.

For flow and dispersion modeling applications, as well as

for mesoscale modeling, it is useful to describe an urban

area or a neighborhood through a small set of parame-

ters rather than explicitly include all buildings.

On the basis of lf (z) and lp(z) parameters, we can

argue that different flow patterns may be expected

within a city. Also, pollution dilution potential of a given

city is linked to city’s breathability a result of the com-

bined effect of flow transport and entrainment within

the city (Buccolieri et al. 2010). This is expected to be

dependent on l(z) parameters, their spatial distribution

(intracity variation) and the vertical building height

variability (e.g., s/H values). The following arguments

clarify the previous statements. We explain how lp and

lf parameters, as well as lf (z) and lp(z) can be used to

extract information about the building distribution of

a city, and the average shape of the ‘‘city’s building en-

velop.’’ The purpose is to show how a combination of

those lambda parameters can be used to capture the

important geometric features of a city, which in turn

influences flow patterns within urban areas or within

specific neighborhoods. First we consider lf and lp, then

we extend the analysis to lf (z) and lp(z).

One way of extracting information about building

shape is by direct evaluation of the lp to lf ratio given by

lp

lf(u)

;B

2

HB5

B

H, (9)

where B is an average value between the width and the

depth of buildings (see Fig. 4) and the overbar indicates

the average over all azimuths. It shows that the combi-

nation of both lambda parameters can be used to de-

termine whether a city has grown more horizontally or

vertically. Based on the lf and lp values in Fig. 8, these

ratios indicate that northern European cities and Salt

Lake City are characterized by buildings with heights

smaller than breadths (ratios between 1.3 and 2) whereas

buildings in southern European cities and Los Angeles,

have heights larger than, or comparable to, their breadths

(ratios between 0.7 and 0.9). Additional information on

the average building shape can be derived from these

ratios as follows.

One may start by considering the ith building of height

Hi, depth Li, and width Wi. Here, Wi always denotes the

horizontal dimension of the building facxade facing the

incoming wind, while Li is the other horizontal di-

mension. Its planar area Ap,i is LiWi. For simplicity, we

assume that the ith building is positioned in such a way

that the building frontal area is just Af,i(u) 5 HiWi. This

simplification is not too restrictive, because one can al-

ways find a wind direction u for which most of buildings

have a facade in the direction perpendicular to the wind.

Then, replacing Ap,i and Af,i with the respective lp and lf

definitions given by Eqs. (1) and (2) yields:

FIG. 11. As in Fig. 10, but for lp(z).



Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

lp

lf(u)

5

�i

LiW

i

�i

HiW

i

5L

W

HW

, (10)

where HW

and LW

are the average building height and

the average depth of buildings weighted by their width,

respectively. Similarly, if we considered the direction

perpendicular to u; that is u?, the frontal area Af,i(u?) is

HiLi and, therefore,

lp

lf(u?)

5

�i

LiW

i

�i

HiL

i

5W

L

HL

. (11)

Consequently, the comparison of these ratios indicates

approximately whether the buildings have square or rect-

angular footprints. By applying the above reasoning to all

cities studied, we conclude that both northern European

cities and Salt Lake City have mainly short rectangular

buildings, while southern European cities and Los Angeles

have mainly cubelike buildings. Even though some care

should be taken in adopting this reasoning, because the

averaging process might lead to wrong conclusions on the

actual building shape, the specific result can be interpreted

as the ‘‘average shape of the neighborhood building en-

velop’’ relevant to the flow. This needs to be appropriately

assessed by detailed flow calculations using for instance

CFD models.

Other observations can be made from the analysis of

lf (z) and lp(z) profiles shown in Fig. 10 and Fig. 11 as

discussed earlier. For example, it is clear that small values

of both lf(z) and lp(z) indicate a low density of buildings

with heights equal to or larger than z. To highlight

similarities and differences of the cities investigated,

FF12 igs. 12a,b show lf (z) and lp(z) profiles normalized with

their corresponding value at the ground level versus el-

evation. The latter has been normalized with Hmax, the

maximum building height. This choice is not arbitrary but

it is relevant fluid dynamically as recently proven by Xie

et al. (2008) who have shown that the tallest buildings

within a neighborhood area have a dominant effect on

the overall drag exerted on the flow. The normalization

with Hmax represents a way of showing how a city’s neigh-

borhood is ‘‘seen’’ by the wind, facilitating the com-

parison with other cities and highlighting features that

are common or not common between them. Looking at

the figures, the difference between U.S. and European

cities is apparent. The former have almost the same pro-

file, while the European cities are characterized by a large

spectrum of profiles. Although, once again any gener-

alization should be avoided, this suggests that these

European cities have different architectural features,

while the two U.S. cities have similar ones. In Fig. 12a,

three layers can be identified: the first layer for z/Hmax ,

0.2, the second one for 0.2 , z/Hmax # 0.6, and the last

one for z/Hmax . 0.6. Near the ground, lf(z) is almost

constant for European cities, while for U.S. cities, this is

the layer where lf (z) varies the most. In the interme-

diate layer, the behavior of lf (z) for European and U.S.

cities is reversed. Finally, at the highest elevations lf(z)

is constant for both U.S. and northern European cities.

Here, only Lecce shows a different shape; that is, lf(z)

keeps on varying. Since lp(z) profiles show the same

features of lf (z) profiles, we can derive important in-

formation about the vertical structure of the cities. The

two U.S. cities can be thought of as having two main

types of buildings: high-rise and very short buildings.

However, the spike of the profiles near the origin shows

that the majority of buildings belong to the second cate-

gory, and only a few high-rise buildings are present. An

opposite configuration appears for the southern European

city, whose profiles confirm the presence of a considerable

number of buildings distributed within a relatively large

range of heights. The northern European cities can be

FIG. 12. Profiles of (a) lf (z) and (b) lp(z) normalized with their

value at ground level. The elevation z is normalized with the

maximum building height, Hmax, of each city.



Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

located between these two limits. London has a profile

more similar to that found for two U.S. cities, because of

the spike near the origin and the presence of a spectrum

of lf values in a restricted range of low z values. The

Toulouse profile shows a similar shape, but is shifted up,

slightly. This fact, and a larger value of lf near the ori-

gin, suggests a slightly larger number of tall buildings.

Finally, Berlin is characterized by a very low variability

of lf and lp, indicative of the most homogenous city

among all those investigated.

We further observe that all European cities have al-

most the same values of H and s/H, but different shapes

of lf (z) profiles. More explicitly lf (z) coupled with lp(z),

incorporates the information contained in s/H, and

provides a description of building height spatial vari-

ability more like the real spatial configuration of a city.

The U.S. cities are characterized by very large values of

s/H, suggesting large building-height variability. How-

ever, lambda profiles show that these cities are rather

homogeneous, despite the large s/H, the result of hav-

ing few high-rise buildings.

The estimation of lp and lf parameters and the analysis

of their profiles versus elevation, suggest how to rep-

resent a city in a compact and effective way. The two

North American cities have a sparse (low values of lp

and lf) canopy of two building heights: tall buildings

(cubelike shape for both), and short (compared their

respective Hmax) buildings (narrow for Los Angeles and

wide for Salt Like City). Southern European cities have

a dense canopy made up of tall (compared to their re-

spective Hmax) cubelike buildings. An intermediate con-

figuration can be hypothesized for the northern European

cities. For example, most buildings in Berlin have similar

heights, with tall and wide buildings characterized by a

low value of lp. For city configurations like this, it be-

comes difficult to conjecture a possible wind regime and

its implication for city breathability. This case requires

a quantitative evaluation of the building effects on flow

and consequently on dispersion characteristics. The pres-

ence of a low spatial building-height variability (a neg-

ative effect with respect to city breathability) and a low

value of built-up area index (positive effect) needs to be

assessed to establish which one is the most dominant by

using, for example, CFD models. Furthermore intracity

variability of morphometry is expected to be relevant

in this context. Cities are made up of different neigh-

borhoods and the ‘‘physical neighborhood’’ might be

identified by its lambda parameters. Possibly, cities

may be better categorized by the types and distribution

of neighborhoods.

The analysis presented in this paper has only hinted on

the possibility of including the effect on the flow due to

intracity variations of the morphometric parameters.

This is strictly dependent on the definition one adopts

for the neighborhoods. Once this is done the lambda

categorization presented here can be used as a frame-

work to interpret the overall effect of the city on the

flow. This aspect is expected to be especially relevant for

large cities (including megacities), which typically in-

corporate many land-use types and require additional

investigations. This is left to future research.

6. Concluding remarks

This paper describes the derivation and analysis of

DEMs, with image processing techniques for a southern

European city of medium size, and their comparison

with other DEMs of portions of three northern Euro-

pean and two North American cities. North–south dif-

ferences have been chosen because they are considered

relevant for their climate characteristics but other choices

can be made to differentiate between city morphometries

without loss of generality.

In general terms, the focus of this work has been to

promote and to improve city DEMs’ analyses, with a

suggestion on how to represent a city in a compact way

within mesoscale and urban flow and dispersion models.

This has required investigating and combining results

from different geographic regions, taking into consid-

eration various aspects ranging from raw building data

collection, image analysis, and their errors with respect

to the building statistics calculations.

In summary this paper has three major contributions.

(i) A new DEM derivation methodology has been

developed and successfully applied to three areas

of Lecce, an example of a southern European–

Mediterranean city. This has required the acquisi-

tion of raw measurements of buildings’ heights

using low cost and low tech techniques.

(ii) Various sensitivity tests have been identified and

used to study the effect of image format and image

resolution on the calculated parameters. Their re-

sults show that a) DEM images should be stored in

a proper file format such as TIFF; b) image reso-

lution affects calculated parameters; c) the correct

image resolution can be chosen, based on the res-

olution that does not alter the lp value. Sensitivity

tests on idealized building arrangements have con-

firmed the reliability of algorithms used to estimate

morphometric parameters. Results from the tests can

be used as benchmark data for real cities’ neighbor-

hoods with similar morphometric features.

(iii) DEM analysis of Lecce and their comparison with

DEMs of parts of three northern European and two

North American cities have been presented and



Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

discussed. Despite the several limitations of the

datasets used (the majority of them do not include

trees, population distribution, etc. and are not large

enough to allow us to determine intracity variabil-

ity of the parameters), these results showed that an

effective parameterization of a real urban canopy

could be derived from the coupling of lf (z) and

lp(z) parameters.

(iv) In particular, the analysis of lambda parameters

and their profiles versus elevation has indicated

that the two North American cities are examples of

sparse canopies, comprised mainly of short (com-

pared with the respective Hmax) buildings. On the

contrary, Lecce is an example of a dense and very

homogenous canopy with tall cubelike buildings,

while the three North European cities appear to fall

into an intermediate configuration.

To further develop this picture, it would be interesting

to expand the statistics by considering both larger areas

of each city and a larger number of cities. Regarding the

latter, the DEM construction methodology described in

this paper could be a useful support to the activity. With

its twin advantages of low cost and low technology, this

method could increase the availability of urban DEMs,

especially in those areas of the world with weaker

economies.

The final, but essential, step in this research is to assess

and validate the ideas reported in this paper, using de-

tailed building resolving flow models, a work in progress

by the authors using CFD models.

Acknowledgments. L. S. Leo, acknowledges the fi-

nancial support given by the SIMPA (Sistema Integrato

per il Monitoraggio del Particolato Atmosferico) Pro-

ject, sponsored by the Apulia Region. The research

described in this project by one of the authors (REB)

was funded in part by the Singapore National Research

Foundation (NRF) through the Singapore–MIT Alli-

ance for Research and Technology (SMART) Center for

Environmental Sensing and Monitoring (CENSAM). We

are deeply grateful to Ms. Chiara Chirizzi, Dr. Riccardo

Buccolieri, Mr. Gennaro Rispoli, and Mr. Massimo

Luggeri for their invaluable help with the building-

height collection. We have greatly benefited from in-

sightful discussions with Dott. Ing. Roberto Perrone,

GIS specialist from the Territorial Planning Department

of Province of Lecce, concerning issues related to the

vector to raster conversion and error handling in carto-

graphic data. We also acknowledge the careful work

made by two anonymous referees who with their in-

sightful and precious comments have helped us to im-

prove the paper substantially.

APPENDIX

Sensitivity Analysis

As described in section 3, the particular image tech-

nique used here poses some questions about the image

processing itself. In particular, it is important to ask the

question whether and how much both the image spatial

resolution and the file format (e.g., JPEG, BMP, TIFF,

GIF) used to store images affect the value of the cal-

culated morphometric parameters. As emphasized in

the methodology section, this is an issue separate from

error treatment in the DEM construction. The sensi-

tivity analysis presented here can be applied whenever

image processing techniques are used. In the following,

several tests were applied to various geometries of dif-

ferent complexity. For each of these configurations,

values of the morphometric parameters were deter-

mined using both our algorithms and theoretical for-

mulations based on purely geometric considerations

[see Eqs. (1), (2), and (4)].

FIG. A1. Results of the image processing algorithms for different

file formats, TIFF, Bmp, GIF, and JPEG. The image DEM_1, of

256 3 256 pixels dimension, represents cubic buildings of 10- and

5-m heights spread on a 400 3 400 m area. The overbar denotes

a value averaged over all azimuths (except for H).



Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

a. Influence of image format

We made a comparison of different file formats of

images of simple cubic arrangements and complex ge-

ometries (including Lecce DEMs). Except for the JPEG

format, the various algorithms always gave the same re-

sults, regardless of their complexity and image resolution.

A simple building configuration is reported in FFA1 ig. A1 as

an example of these comparative analyses. From those

tests TIFF was the preferred format for both the DEMs of

Lecce areas and for sensitivity tests on the image reso-

lution discussed in the next subsection.

b. Influence of image resolution

In addition to establishing which file formats were

the most appropriate, sensitivity analyses enabled us to

confirm the validity of algorithms and most importantly

to investigate the influence of image resolution on the

morphometric parameters. Several tests showed that

even though no general relationship can be found, the

image resolution always affected calculated parameters.

Not all parameters were affected in the same way: as

resolution increased, the lp value tended to agree with

its theoretical value very quickly. Instead, lf and con-

sequently z0 behaved nonlinearly with the image reso-

lution for a fixed wind direction.

For example, F FA2ig. A2 is a simple configuration of cubic

buildings of 16- and 32-m heights on a 400 3 400 m area.

The image dimensions range from 200 3 200 pixels to

3200 3 3200 pixels. For this image, named DEM_2, lp

agreed with its theoretical value on the second signifi-

cant digit at the resolution of 40 pixel cm21; that is, for

FIG. A2. Results (denoted with the subscript algAU10 ) of the image processing algorithms using

different resolutions (in pixels) of the DEM_2. Theoretical values (denoted with the subscript

theor) are also reported. The overbar denotes a value averaged on all azimuths (except for H),

in the other cases the values are calculated for wind coming from the North.

FIG. A3. As in Fig. A2, but for DEM_3.



Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

a pixel size equal to half the accuracy of planar building

data. Instead, the lf values agreed with its theoretical

value on the second significant digit at much higher

resolution. At this resolution, the value of roughness

length is different from its theoretical prediction by 1%.

These discrepancies arise because the lf algorithm is

based on detection of building edges. The smaller the

pixel, the better building contours are detected.

Another example is image DEM_3 (FFA3 ig. A3). Again,

lp agreed with its theoretical prediction on the second

significant digit at a resolution of 40 pixel cm21. How-

ever, the agreement of lf, zd, and z0 with their theoret-

ical values got worse. The cause of this is the presence of

many buildings with oblique edges. One should bear in

mind that the treatment of oblique segments within

a raster image is always a source of large errors in

comparison to straight segments or lines. An example of

this is shown in FFA4 ig. A4, where building facades have

been rotated with respect to the external frame. More

specifically, in the first case, represented by the DEM_2b,

we used DEM_2 of Fig. A2 but with a wind direc-

tion equal to 458. In the second case we used DEM_4 of

FIG. A4. Results of the image processing algorithms using different resolutions (pixels) of the

DEM_2b and DEM_4. Theoretical values (denoted with the subscript theor) are also reported.

The values are calculated for northeasterly winds in DEM_2b and northerly winds in DEM_4.

TABLE 2. Average mean building height (h) and planar area

weighted building height (H) and correspondent standard devia-

tions calculated with ArcView and their comparison with algorithm

(Matlab) results. Comparison for lp values is also listed.

Parameters

Le1 (180

pixel cm21)

Le2 (300

pixel cm21)

Le3 (300

pixel cm21)

h (m) (ArcView) 16 10 15

sh (m) (ArcView) 9 6 4

H (m) (ArcView) 17 12 14

s (m) (ArcView) 9 6 4

H (m) (Matlab) 17 12 15

s (m) (Matlab) 8 7 5

lp (ArcView) 0.443 0.380 0.405

lp (Matlab) 0.444 0.382 0.408



Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

Fig. A4. DEM_4 is just DEM_2 rotated of 458. In this

case the wind is coming from the north. Results for some

sensitive morphometric parameters are compared in

Fig. A4. Even though the original DEM is the same, the

change of the building orientation has led to more dis-

agreement between lf and z0 predictions and their the-

oretical values.

In conclusion, the sensitivity analysis showed that it is

always suitable to rotate the DEM to get the largest

number of facades parallel to the external frame of the

image. Once this is done, it is necessary to identify the

threshold of the ‘‘correct’’ resolution for each DEM

image to proceed with the calculation of the morpho-

metric parameters.

On the other hand, when the method is applied to

complex urban textures, it becomes difficult to calculate

the theoretical values of many of these morphometric

parameters and consequently it is not possible to establish

the level of accuracy of lp, lf, and the other parameters at

a given resolution. A possible solution to evaluate the

accuracy of the results is to choose lp as a control vari-

able. This can be done because its theoretical calculation

is generally easier than other parameters and can be de-

rived in other ways. For example, ArcView allows one to

extract the lp parameter in a very simple way.

Consequently, one could select that resolution for

which the discrepancy between the calculated and the

theoretical value of lp is of the order of 0.1%–0.2%. At

this resolution, the values of lf will agree with its theo-

retical prediction on the second significant digit. In this

case, z0 will differ from the theoretical value only by

1%–2%. For lower resolutions, these parameters should

be considered reliable only on the first significant digit.

Based on Lecce DEMs analyses, we conclude that in

general if lp agreed with its theoretical value on the

second significant digit, statistical parameters are always

calculated accurately. The theoretical values of lp for

the Lecce DEMs were calculated by ArcView and are

listed in Table 1.

With ArcView, we also calculated the average H and

standard deviation s of buildings’ heights with Eqs. (4)

and (5). Just for comparison, we also calculated the

nonarea-weighted building-height h and corresponding

standard deviation sh:

h 5

�N

iH

i

N,

sh

5

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�

i(H

i� h)2

N � 1

vuut.

These results are reported in T T2able 2 and are com-

pared with the values extracted by the algorithms with

Matlab. There, we also listed the lp values obtained by

ArcView, and for these cases we verified that to achieve

an agreement of about 0.1%–0.2% between the calcu-

lated and the theoretical valued of lp, 3600 3 3600 pixels

were required for Le1 image and 6000 3 6000 pixels for

both Le2 and Le3 images.

REFERENCES

Baltsavias, E. P., 1999: Airborne laser scanning: basic relations and

formulas. J. Photogramm. Remote Sens., 54, 199–214.

Belcher, S. E., N. Jerram, and J. C. R. Hunt, 2003: Adjustment of

a turbulent boundary layer to a canopy of roughness elements.

J. Fluid Mech., 488, 369–398.

Bolle, H. J., 2003: Mediterranean Climate: Variability and Trends.

Springer, 372 pp.

Britter, R. E., and S. R. Hanna, 2003: Flow and dispersion in urban

areas. Annu. Rev. Fluid Mech., 35, 469–496.

Brown, M., 2000: Urban parameterizations for mesoscale models.

Mesoscale Atmospheric Dispersion, Z. Boybeyi, Ed., WIT

Press, 193–255.

Buccolieri, R., M. Sandberg, and S. Di Sabatino, 2010: City

breathability and its link to pollutant concentration distribution

within urban-like geometries. Atmos. Environ., 44, 1894–1903.

Burian, S. J., M. J. Brown, and S. P. Linger, 2002: Building mor-

phology analysis of downtown Los Angeles, California. Tech.

Rep. LA-UR-02-0781, 67 pp.

Burian, S., M. J. Brown, J. Ching, M. L. Cheuk, M. Yuan, W. Han,

and A. McKinnon, 2004: Urban morphological analysis for

mesoscale meteorological and dispersion modeling applica-

tions: Current issues. Proc. Fifth Symp. Urban Environment,

Vancouver, BC, Canada, Amer. Meteor. Soc., paper 9.1.

——, I. Uugustus, I. Jeyachandran, and M. J. Brown, 2007: National

Buildings Statistics Database: Version 2. LA-UR-08-1921, 82 pp.

Camuffo, D., C. Secco, P. Brimblecombe, and J. Martin-Vide, 2000:

Sea storms in the Adriatic Sea and the Western Mediterranean

during the last millennium. Climatic Change, 46, 209–223.

Ching, J., and Coauthors, 2009: National Urban Database and

Access Portal Tool (NUDAPT). Bull. Amer. Meteor. Soc., 90,1157–1168.

Cionco, R., and R. Ellefsen, 1998: High resolution urban mor-

phology data for urban wind flow modeling. Atmos. Environ.,

32, 7–17.

Di Sabatino, S., E. Solazzo, P. Paradisi, and R. E. Britter, 2008: A

simple model for spatially-averaged wind profiles within and

above an urban canopy. Bound.-Layer Meteor., 127, 131–151.

Grimmond, C. S. B., and C. Souch, 1994: Surface description for

urban climate studies: a GIS based methodology. Geocarto

Int., 9, 47–59.

——, and T. R. Oke, 1999: Aerodynamic properties of urban areas

derived from analysis of surface form. J. Appl. Meteor., 38,

1262–1292.

Kastner-Klein, P., R. Berkowicz, and R. E. Britter, 2004: The in-

fluence of street architecture on flow and dispersion in street

canyons. Meteor. Atmos. Phys., 87, 121–131.

Long, N., S. Kermadi, C. Kergomard, P. G. Mestayer, and

A. Trebouet, 2003: Urban cover modes and thermodynamic

parameters from urban database and satellite data: A com-

parison for Marseille during ESCOMPTE. Proc. Fifth Int.

Conf. Urban Climate, qodz, Poland, paper 8.3 AU5.



Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

Macdonald, R. W., 2000: Modelling the mean velocity profile in the

urban canopy layer. Bound.-Layer Meteor., 97, 25–45AU6 .

XXXX, 1997: MATLAB. The Math Works IncAU7 .

Martilli, A., A. Clappier, and M. W. Rotach, 2000: A parameter-

isation of the urban effects for mesoscale models. Proc. Third

Symp. Urban Environment, Davis, CA, Amer. Meteor. Soc.,

131–132.

Muller, C., S. Burian, and M. J. Brown, 1999: Urban database is-

sues. Tech. Rep. LA-UR-99-5874, 10 ppAU8 .

Oke, T. R., 1988: Street design and urban canopy layer climate.

Energy Build., 11, 103–113.

Otte, T., A. Lacser, S. Dupont, and J. Ching, 2004: Implementation

of an urban canopy parameterization in a mesoscale meteo-

rological model. J. Appl. Meteor., 43, 1648–1665.

Ratti, C., and P. Richens, 2004: Raster analysis of urban form.

Environ. Plan. B Plan. Des., 31, 297–309.

Ratti, C. F., S. Di Sabatino, F. Caton, and R. E. Britter, 2000:

Morphological parameters for urban dispersionAU11 models. Proc.

Third Symp. Urban Environment, Davis, CA, Amer. Meteor.

Soc., paper 2.3.

Ratti, C., S. Di Sabatino, R. E. Britter, M. J. Brown, F. Caton, and

S. Burian, 2002: Analysis of 3-D urban databases with respect

to air pollution dispersion for a number of European and

American cities. Water Air Soil Pollut. Focus, 2, 459–469.

——, ——, and ——, 2006: Urban texture analysis with image

processing techniques: winds and dispersion. Theor. Appl.

Climatol., 84, 77–90.

Raupach, M. R., 1994: Simplified expressions for vegetation rough-

ness length and zero-plane displacement as functions of canopy

height and area index. Bound.-Layer Meteor., 71, 211–216.

Tacket, N. D., S. M. Howarth, and R. E. Burge, 1991: A model for

the imaging of urban areas by synthetic aperture radar. IEEE

Trans. Geosci. Remote Sens., 20, 432–443.

Xie, Z.-T., O. Coceal, and I. Castro, 2008: Large-eddy simulation

of flows over random urban-like obstacles. Bound.-Layer

Meteor., 129, 1–23.



Jour

nal o

f App

lied

Met

eoro

logy

and

Clim

atol

ogy

(Pro

of O

nly)

Documents

This paper might be a pre-copy-editing or a post-print ...senseable.mit.edu/papers/pdf/20100701_DiSabatino... · partimento di Scienza deiMateriali, Laboratoriodi Climatologia e Meteorologia,